First you will need to have some sort of network infrastructure in your office. You probably already have that .
One component will be your router. All you computers will connect to it via wireless or by physical cable.
You could have your server connect via wireless, however I would recommend that you use a physical wired connection, mainly because you will have better bandwidth.
The security aspect can be taken care of, as long as you set appropriate passwords and file permissions. Your greatest security problem will be from people inside you company. If your router is protected then your internal network is safe enough.
I would recommend that you look at a dedicated NAS storage box rather than a general purpose computer as it wil be easier to set up and maintain.
Something like Synology DS918+
For your disks You should consider raid 1 or raid 10 configuration (never raid 5 or raid0).
Remember to back your data up somewhere.